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%I #10 Dec 21 2023 15:15:48
%S 2,4,3,8,10,4,16,36,24,6,32,136,176,70,8,64,528,1376,1044,208,14,128,
%T 2080,10944,16456,6560,700,20,256,8256,87424,262416,209728,43800,2344,
%U 36,512,32896,699136,4195360,6710912,2796976,299600,8230,60
%N Table read by antidiagonals downward: T(n,k) is the number of tilings of the n X k cylinder by two distinct tiles.
%H Peter Kagey, <a href="/A368264/a368264.pdf">Illustration of T(2,3)=36</a>
%H Peter Kagey and William Keehn, <a href="https://arxiv.org/abs/2311.13072">Counting tilings of the n X m grid, cylinder, and torus</a>, arXiv: 2311.13072 [math.CO], 2023.
%e Table begins:
%e n\k| 1 2 3 4 5 6
%e ---+-------------------------------------------
%e 1 | 2 4 8 16 32 64
%e 2 | 3 10 36 136 528 2080
%e 3 | 4 24 176 1376 10944 87424
%e 4 | 6 70 1044 16456 262416 4195360
%e 5 | 8 208 6560 209728 6710912 214748416
%e 6 | 14 700 43800 2796976 178962784 11453291200
%t A368264[n_, m_] := 1/n (DivisorSum[n, EulerPhi[#]*2^(n*m/#) &])
%Y Cf. A117401, A368257, A368259, A368261, A368263.
%K nonn,tabl
%O 1,1
%A _Peter Kagey_, Dec 21 2023
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